TL;DR
This paper explores a deformation of canonical anticommutation relations, revealing a structure connected to quasi-hermitian quantum mechanics and demonstrating that many assumptions from similar bosonic cases are automatically satisfied.
Contribution
It extends previous work on deformations of commutation relations to anticommutation relations, showing the construction's simplicity and its relation to quasi-hermitian quantum mechanics.
Findings
Most assumptions from the bosonic case are automatically satisfied.
The construction is more straightforward for anticommutation relations.
Examples include bi-coherent states related to quasi-hermitian quantum mechanics.
Abstract
In a recent series of papers we have analyzed a certain deformation of the canonical commutation relations producing an interesting functional structure which has been proved to have some connections with physics, and in particular with quasi-hermitian quantum mechanics. Here we repeat a similar analysis starting with the canonical anticommutation relations. We will show that in this case most of the assumptions needed in the former situation are automatically satisfied, making our construction rather {\em friendly}. We discuss some examples of our construction, again related to quasi-hermitian quantum mechanics, and the bi-coherent states for the system.
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